code: def local_edge_connectivity(
      G,
      s,
      t,
      flow_func=None,
      auxiliary=None,
      residual=None,
      cutoff=None,
  ):
      r"""Returns local edge connectivity for nodes s and t in G.
  
      Local edge connectivity for two nodes s and t is the minimum number
      of edges that must be removed to disconnect them.
  
      This is a flow based implementation of edge connectivity. We compute the
      maximum flow on an auxiliary digraph build from the original
      network (see below for details). This is equal to the local edge
      connectivity because the value of a maximum s-t-flow is equal to the
      capacity of a minimum s-t-cut (Ford and Fulkerson theorem) [1]_ .
  
      Parameters
      ----------
      G : NetworkX graph
          Undirected or directed graph
  
      s : node
          Source node
  
      t : node
          Target node
  
      flow_func : function
          A function for computing the maximum flow among a pair of nodes.
          The function has to accept at least three parameters: a Digraph,
          a source node, and a target node. And return a residual network
          that follows NetworkX conventions (see :meth:`maximum_flow` for
          details). If flow_func is None, the default maximum flow function
          (:meth:`edmonds_karp`) is used. See below for details. The
          choice of the default function may change from version
          to version and should not be relied on. Default value: None.
  
      auxiliary : NetworkX DiGraph
          Auxiliary digraph for computing flow based edge connectivity. If
          provided it will be reused instead of recreated. Default value: None.
  
      residual : NetworkX DiGraph
          Residual network to compute maximum flow. If provided it will be
          reused instead of recreated. Default value: None.
  
      cutoff : integer, float, or None (default: None)
          If specified, the maximum flow algorithm will terminate when the
          flow value reaches or exceeds the cutoff. This only works for flows
          that support the cutoff parameter (most do) and is ignored otherwise.
  
      Returns
      -------
      K : integer
          local edge connectivity for nodes s and t.
  
      Examples
      --------
      This function is not imported in the base NetworkX namespace, so you
      have to explicitly import it from the connectivity package:
  
      >>> from networkx.algorithms.connectivity import local_edge_connectivity
  
      We use in this example the platonic icosahedral graph, which has edge
      connectivity 5.
  
      >>> G = nx.icosahedral_graph()
      >>> local_edge_connectivity(G, 0, 6)
      5
  
      If you need to compute local connectivity on several pairs of
      nodes in the same graph, it is recommended that you reuse the
      data structures that NetworkX uses in the computation: the
      auxiliary digraph for edge connectivity, and the residual
      network for the underlying maximum flow computation.
  
      Example of how to compute local edge connectivity among
      all pairs of nodes of the platonic icosahedral graph reusing
      the data structures.
  
      >>> import itertools
      >>> # You also have to explicitly import the function for
      >>> # building the auxiliary digraph from the connectivity package
      >>> from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity
      >>> H = build_auxiliary_edge_connectivity(G)
      >>> # And the function for building the residual network from the
      >>> # flow package
      >>> from networkx.algorithms.flow import build_residual_network
      >>> # Note that the auxiliary digraph has an edge attribute named capacity
      >>> R = build_residual_network(H, "capacity")
      >>> result = dict.fromkeys(G, dict())
      >>> # Reuse the auxiliary digraph and the residual network by passing them
      >>> # as parameters
      >>> for u, v in itertools.combinations(G, 2):
      ...     k = local_edge_connectivity(G, u, v, auxiliary=H, residual=R)
      ...     result[u][v] = k
      >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
      True
  
      You can also use alternative flow algorithms for computing edge
      connectivity. For instance, in dense networks the algorithm
      :meth:`shortest_augmenting_path` will usually perform better than
      the default :meth:`edmonds_karp` which is faster for sparse
      networks with highly skewed degree distributions. Alternative flow
      functions have to be explicitly imported from the flow package.
  
      >>> from networkx.algorithms.flow import shortest_augmenting_path
      >>> local_edge_connectivity(G, 0, 6, flow_func=shortest_augmenting_path)
      5
  
      Notes
      -----
      This is a flow based implementation of edge connectivity. We compute the
      maximum flow using, by default, the :meth:`edmonds_karp` algorithm on an
      auxiliary digraph build from the original input graph:
  
      If the input graph is undirected, we replace each edge (`u`,`v`) with
      two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute
      'capacity' for each arc to 1. If the input graph is directed we simply
      add the 'capacity' attribute. This is an implementation of algorithm 1
      in [1]_.
  
      The maximum flow in the auxiliary network is equal to the local edge
      connectivity because the value of a maximum s-t-flow is equal to the
      capacity of a minimum s-t-cut (Ford and Fulkerson theorem).
  
      See also
      --------
      :meth:`edge_connectivity`
      :meth:`local_node_connectivity`
      :meth:`node_connectivity`
      :meth:`maximum_flow`
      :meth:`edmonds_karp`
      :meth:`preflow_push`
      :meth:`shortest_augmenting_path`
  
      References
      ----------
      .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
          http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
  
      """
      if flow_func is None:
          flow_func = default_flow_func
  
      if auxiliary is None:
          H = build_auxiliary_edge_connectivity(G)
      else:
          H = auxiliary
  
      kwargs = {"flow_func": flow_func, "residual": residual}
      if flow_func is shortest_augmenting_path:
          kwargs["cutoff"] = cutoff
          kwargs["two_phase"] = True
      elif flow_func is edmonds_karp:
          kwargs["cutoff"] = cutoff
      elif flow_func is dinitz:
          kwargs["cutoff"] = cutoff
      elif flow_func is boykov_kolmogorov:
          kwargs["cutoff"] = cutoff
  
      return nx.maximum_flow_value(H, s, t, **kwargs)
  
file_path: networkx/networkx/algorithms/connectivity/connectivity.py
imports: import itertools
  from operator import itemgetter
  import networkx
  from networkx.algorithms.flow import boykov_kolmogorov, build_residual_network, dinitz, edmonds_karp, shortest_augmenting_path
  from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity
label_desc: Use image node_id 5 for calling a global function with example usage: local_edge_connectivity(G, s, t, flow_func, auxiliary, residual, cutoff) and returns: nx